Orthogonal polynomials in two variables and second-order partial differential equations

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We study the second-order partial differential equations L[u] = Au-xx + 2Bu(xy) + Cu-yy + Du(x) + Eu-y = lambda(n)u, which have orthogonal polynomials in two variables as solutions. By using formal functional calculus on moment functionals, we first give new simpler proofs and improvements of the results by Krall and Sheffer and Littlejohn. We then give a two-variable version of Al-Salam and Chihara's characterization of classical orthogonal polynomials in one variable. We also study in detail the case when L[.] belongs to the basic class, that is, A(y) = C-x = 0. In particular, we characterize all such differential equations which have a product of two classical orthogonal polynomials in one variable as solutions.
Publisher
ELSEVIER SCIENCE BV
Issue Date
1997
Language
English
Article Type
Article; Proceedings Paper
Citation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.82, no.1-2, pp.239 - 260

ISSN
0377-0427
URI
http://hdl.handle.net/10203/69191
Appears in Collection
MA-Journal Papers(저널논문)
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